This is usually said to be from ad "to" (see ad-) + a stem meaning "tail," from a PIE *ul- "the tail" (source also of Sanskrit valah "tail-hair," and Lithuanian valai "horse's tail"). The original notion would be "to wag the tail" like a fawning dog (compare Greek sainein "to wag the tail," also "to flatter;" also see wheedle). But de Vaan finds phonetic problems with these and concludes the etymology is uncertain, though he proposes a connection with avidus "eager," via *adulo- "who is eager toward something," hence "a flatterer." Adulation may proceed from true blind worship or be insincere, from hope of advantage.